question_answer 29)

                  Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because,                 (a) the solar cells and batteries in satellites run out.                 (b) the laws of gravitation predict a trajectory spiralling inwards.                 (c) of viscous forces causing the speed of satellite and hence height to gradually decrease.                 (d) of collisions with other satellites.

Answer:

                  (c) Centripetal force needed by satellite,                 \[\frac{m{{v}^{2}}}{r}\,=\,\frac{GMm}{{{r}^{2}}}\] or \[{{\upsilon }^{2}}=\frac{GM}{r}\] ? (i)                 Total energy of satellite at a distance \[{{r}_{2}}\]  from the centre of the earth, \[E=-\frac{GMm}{{{r}^{2}}}\].                 Viscous force acting on satellite decreases energy of the satellite. It is possible if r decreases. Thus, velocity of satellite increases.